If lines x = ay + b, z = cy + d and x = a'z + b', y = c'z +… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 9 Jan · Shift II

If lines

x = ay + b

z = cy + d

and

x = a'z + b'

y = c'z + d'

are perpendicular, then

A.
$ab' + bc' + 1 = 0$
B.
$bb' + cc' + 1 = 0$
C.
$aa' + c + c' = 0$
D.
$cc' + a + a' = 0$

Show answer and solution

Correct option: C

Solution

The first line can be written with y as parameter: direction ratios are (a, 1, c).

The second line with z as parameter: x = a'z + b', y = c'z + d', so direction ratios are (a', c', 1).

For perpendicularity, the dot product of direction vectors = 0:
a·a' + 1·c' + c·1 = 0
→ aa' + c' + c = 0, i.e., aa' + c + c' = 0.

[JEE Main 2019 · 9 Jan · Shift II]

Practise Straight Lines and Pair of Lines the way it is asked

A timed set of real JEE Main Straight Lines and Pair of Lines questions, graded as the exam grades. No sign-up.

Start a Straight Lines and Pair of Lines test

More: all JEE Main Straight Lines and Pair of Lines questions · JEE Main 2019 · Mathematics chapter list

JEE Main 2019 Mathematics question on Straight Lines and Pair of Lines